If I'm reading the problem right, you need to reduce the product of cos^3 * sin^4 into just powers of cos? right? Well you are making the problem too hard by trying to do anything with cos^3. It is already a power of cos, so you don't need to do anything with it. This is why you are coming around full circle back to cos^3 on that part. In your solution for sin^4, you have a line that is all cos. Stop there. Don't try to put sin back in after that. All that's left is to mutiply that through by cos^3.